Martin solved the quadratic equation 3x2+2x−8=0
. His work is shown below. However, he accidentally spilled ink over the step where he divided by the GCF that he found for each pair. Which of the following options shows the missing part of Martin’s work?
Several lines of equations.
(1 point)
Responses
3x(x+2)+4(x+2)=0
3 x left parenthesis x plus 2 right parenthesis plus 4 left parenthesis x plus 2 right parenthesis equals 0
3x(x+2)−4(x+2)=0
3 x left parenthesis x plus 2 right parenthesis minus 4 left parenthesis x plus 2 right parenthesis equals 0
3x(x+2)−4(x−2)=0
3 x left parenthesis x plus 2 right parenthesis minus 4 left parenthesis x minus 2 right parenthesis equals 0
x(3x+6)+4(x+2)=0
x(3x+6)+4(x+2)=0
To solve the quadratic equation 3x^2 + 2x - 8 = 0, we need to factorize or use the quadratic formula. From the given options, it seems like Martin used the factoring method.
Let's go through each option and see which one is correct.
Option 1:
3x(x+2) + 4(x+2) = 0
In this step, Martin factored the equation by finding the greatest common factor (GCF) for each pair of terms. The GCF of 3x and 2x is x, and the GCF of 2 and -8 is 2. By factoring out these GCFs, Martin rewrote the equation as shown above.
Option 2:
3x(x+2) - 4(x+2) = 0
This option doesn't match with the given problem since Martin accidentally spilled ink over the step where he divided by the GCF. The sign in front of the term -4 is incorrect.
Option 3:
3x(x+2) - 4(x-2) = 0
This option is not correct either since Martin accidentally spilled ink over the step where he divided by the GCF. The last term should be (x+2) instead of (x-2).
Option 4:
x(3x+6) + 4(x+2) = 0
This option doesn't match with the given problem since it is not the same equation. Martin's original equation was 3x^2 + 2x - 8 = 0, not x(3x+6) + 4(x+2) = 0.
Therefore, the correct missing part of Martin's work is:
3x(x+2) + 4(x+2) = 0
The missing part of Martin's work is:
3x(x+2) − 4(x+2) = 0
Explanation:
To find the missing part, we need to divide each term by the greatest common factor (GCF) of the expression. In this case, the GCF is (x+2). So, we divide each term by (x+2).
By dividing each term by (x+2), we get:
3x(x+2) / (x+2) - 4(x+2) / (x+2) = 0
This simplifies to:
3x − 4 = 0
Therefore, the missing part of Martin's work is:
3x(x+2) − 4(x+2) = 0.